The invention relates to cylindrical well screens and particularly to fittings for such screens which are used to attach one screen to another or to a length of pipe. A conventional well screen of the type shown in Johnson U.S. Pat. No. 2,046,457 has a trapezoidal-shaped surface-forming wire spirally wound about a plurality of longitudinal support rods to which it is welded at every joint. Preferably, a screen should have a substantial tensile strength to resist the forces applied to it from underlying elements in a pipe string or when the screen is being removed from a well and such strength is, of course, provided only by the longitudinal support rods. However, even where such rods are produced by cold-rolling and work-hardening to provide tensile strengths in excess of 150,000 psi, the act of welding the ends of the rods to a fitting member produces an annealing of the rods which effectively destroys the strength increase gained by the initial work-hardening. U.S. Pat. No. 2,682,309 shows a fitting being threaded and/or brazed to the support bars of a screen beyond its slotted region. U.S. Pat. No. 1,862,838 also shows a fitting threaded to the support rods beyond the wrapped wire slotted region. The thread grooves in the rods for the fitting are of identical pitch to the grooves provided for the wrap wire. An internal longitudinally slotted, cylindrical sleeve backs up the rod ends in the region opposite the fitting.